107,736 research outputs found
Biomechanical Surrogate Modelling Using Stabilized Vectorial Greedy Kernel Methods
No full textGreedy kernel approximation algorithms are successful techniques for sparse and accurate data-based modelling and function approximation. Based on a recent idea of stabilization (Wenzel et al., A novel class of stabilized greedy kernel approximation algorithms: convergence, stability & uniform point distribution. e-prints. arXiv:1911.04352, 2019) of such algorithms in the scalar output case, we here consider the vectorial extension built on VKOGA (Wirtz and Haasdonk, Dolomites Res Notes Approx 6:83–100, 2013. We introduce the so called γ-restricted VKOGA, comment on analytical properties and present numerical evaluation on data from a clinically relevant application, the modelling of the human spine. The experiments show that the new stabilized algorithms result in improved accuracy and stability over the non-stabilized algorithms
Strebla paramirabilis Wenzel 1976
No full textparamirabilis Wenzel, 1976: 158, figs 60 C, 64 F. Type locality: Venezuela, T. F. Amazonas, Cabacera del Caño Culebra, 40 km NW Esmeralda, 1,140 m. Type host: Artibeus jamaicensis (= Artibeus amplus see Handley, 1987). HT M, AT F (USNM), PT 21 M, 16 F (FMNH). Distr.: Colombia (Meta (El Parque La Macarena, Refugio, 100 m W; Cano, Cabana Refugio, 80 m W)), Bolivia, Ecuador, Peru, Venezuela. Refs.: Wenzel, 1976: 158; Guerrero, 1996: 14 (cat.); Autino et al., 2011: 918; FMNH, 2014.Published as part of Dick, Carl W., Graciolli, Gustavo & Guerrero, Ricardo, 2016, FAMILY STREBLIDAE, pp. 784-802 in Zootaxa 4122 (1) on page 789, DOI: 10.11646/zootaxa.4122.1.67, http://zenodo.org/record/26415
Trichobius diaemi Wenzel 1976
No full textdiaemi Wenzel, 1976: 68, figs 23 C, 26 J. Type locality: Venezuela, T. F. Amazonas, Puerto Ayacucho, Rio Manapiare. Type host: Diaemus youngi Jentink (= Desmodus youngii Jentink). HT M, AT F (USNM); PT 107 (FMNH, UCV). Distr.: Colombia Guainia (Cerca Amanaven), Brazil, Paraguay, Peru, Trinidad, Venezuela. Refs.: Wenzel, 1976: 68; Guerrero, 1995 a: 14 (cat.), 1997: 10 (cat.); Dick & Gettinger, 2005: 1020; Aguiar et al., 2006: 895; FMNH, 2014.Published as part of Dick, Carl W., Graciolli, Gustavo & Guerrero, Ricardo, 2016, FAMILY STREBLIDAE, pp. 784-802 in Zootaxa 4122 (1) on page 795, DOI: 10.11646/zootaxa.4122.1.67, http://zenodo.org/record/26415
Letter, [Author unclear] to Paulina T. Merritt
No full textHandwritten letter to Paulina Merritt from an unknown author, October 1, 1876.
DATA-DRIVEN KERNEL DESIGNS FOR OPTIMIZED GREEDY SCHEMES: A MACHINE LEARNING PERSPECTIVE
No full textThanks to their easy implementation via radial basis functions (RBFs), meshfree kernel methods have proved to be an effective tool for, e.g., scattered data interpolation, PDE collocation, and classification and regression tasks. Their accuracy might depend on a length scale hyperparameter, which is often tuned via cross-validation schemes. Here we leverage approaches and tools from the machine learning community to introduce two-layered kernel machines, which generalize the classical RBF approaches that rely on a single hyperparameter. Indeed, the proposed learning strategy returns a kernel that is optimized not only in the Euclidean directions, but that further incorporates kernel rotations. The kernel optimization is shown to be robust by using recently improved calculations of cross-validation scores. Finally, the use of greedy approaches, and specifically of the vectorial kernel orthogonal greedy algorithm (VKOGA), allows us to construct an optimized basis that adapts to the data. Beyond a rigorous analysis on the convergence of the so-constructed two-layered (2L)-KOGA, its benefits are highlighted on both synthesized and real benchmark datasets
Analysis of structured deep kernel networks
No full textIn this paper, we leverage a recent deep kernel representer theorem to connect kernel based learning and (deep) neural networks in order to understand their interplay. In particular, we show that the use of special types of kernels yields models reminiscent of neural networks that are founded in the same theoretical framework of classical kernel methods, while benefiting from the computational advantages of deep neural networks. Especially the introduced Structured Deep Kernel Networks (SDKNs) can be viewed as neural networks (NNs) with optimizable activation functions obeying a representer theorem. This link allows us to analyze also NNs within the framework of kernel networks. We prove analytic properties of the SDKNs which show their universal approximation properties in three different asymptotic regimes of unbounded number of centers, width and depth. Especially in the case of unbounded depth, more accurate constructions can be achieved using fewer layers compared to corresponding constructions for ReLU neural networks. This is made possible by leveraging properties of kernel approximation
Analysis of Target Data-Dependent Greedy Kernel Algorithms: Convergence Rates for f-, f⋅P- and f/P-Greedy
No full textData-dependent greedy algorithms in kernel spaces are known to provide fast converging interpolants, while being extremely easy to implement and efficient to run. Despite this experimental evidence, no detailed theory has yet been presented. This situation is unsatisfactory, especially when compared to the case of the data-independent P-greedy algorithm, for which optimal convergence rates are available, despite its performances being usually inferior to the ones of target data-dependent algorithms. In this work, we fill this gap by first defining a new scale of greedy algorithms for interpolation that comprises all the existing ones in a unique analysis, where the degree of dependency of the selection criterion on the functional data is quantified by a real parameter. We then prove new convergence rates where this degree is taken into account, and we show that, possibly up to a logarithmic factor, target data-dependent selection strategies provide faster convergence. In particular, for the first time we obtain convergence rates for target data adaptive interpolation that are faster than the ones given by uniform points, without the need of any special assumption on the target function. These results are made possible by refining an earlier analysis of greedy algorithms in general Hilbert spaces. The rates are confirmed by a number of numerical examples
A novel class of stabilized greedy kernel approximation algorithms: Convergence, stability and uniform point distribution
No full textKernel based methods provide a way to reconstruct potentially high-dimensional functions from meshfree samples, i.e., sampling points and corresponding target values. A crucial ingredient for this to be successful is the distribution of the sampling points. Since the computation of an optimal selection of sampling points may be an infeasible task, one promising option is to use greedy methods.
Although these methods may be very effective, depending on the specific greedy criterion the chosen points might quickly lead to instabilities in the computation. To circumvent this problem, we introduce and investigate a new class of stabilized greedy kernel algorithms, which can be used to create a scale of new selection strategies.
We analyze these algorithms, and in particular we prove convergence results and quantify in a precise way the distribution of the selected points. These results allow to prove, in the case of certain Sobolev kernels, that the algorithms have optimal stability and optimal convergence rates, including for functions outside the native space of the kernel. The results also apply to the case of the usual -greedy algorithm, significantly improving state-of-the-art results available in the literature. Illustrative experiments are presented that support the theoretical findings and show improvements of the stabilized algorithms in terms of accuracy due to improved stability
Ordinis Jvridici Vitembergensis p. t. Decanvs Jo. Balthasar Wernher, Jc. Potentissimo Poloniarvm Regi Et Electori Saxoniae A Consiliis Avlae Atqve Jvstitiae, Ordinarivs Academiae, Et Antecessor Primarivs Etc. Lectori S. D. : [P. P. Vitembergæ Dominica XXIII. p. Trinit. A. MDCCXVIII.]
No full textEinladung zur jur. Disputation von Christoph Gottlieb Wenzel, November 1718. - Enth. Lebenslauf des KandidatenWittenberg, Univ., Univ.-Progr., 1718Autopsie nach Ex. der ULB Sachsen-AnhaltVorlageform des Kolophons: Literis Gerdesianis. - Erscheinungsjahr nach Datierung am Textende bestimm
Handwritten biographical information on Paulina T. McClung Merritt
No full textA handwritten biography of Paulina T. McClung Merritt by an unknown author, 1892.
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